Question

The quadratic polynomial,the sum and product of whose zeroes are -3 and 2, is​

Answer 1

Answer:

x² + 3x + 2

Step-by-step explanation:

Given,

Sum = -3

Product = 2

Let the zeroes be a and b

a + b = -3

ab = 2

so, the quadratic equation is....

x² - (a + b)x + ab

= x² - (-3)x + 2

= x² + 3x + 2

You might think how I got (x² - (a + b)x + ab) this equation

I will show you the proof if in case you dont know

Let the Quadratic equation be

ax² + bx + c = 0

Dividing whole equation by a we get

x² + (b/a)x + (c/a) = 0

Now let A and B be the zeroes of the Quadratic equation x² + (b/a)x + c/a = 0 -----1

Thus x = A and x = B

thus, factors will be (x - A) and (x - B)

(x - A)(x - B) = 0

x² - Bx - Ax + AB = 0

x² - (A + B)x + AB = 0 ------2

Now if we were to compare eq.1 and eq.2 we get

-(A + B) = b/a

A + B = -b/a

AB = c/a

Thus,

Sum of Zeroes = -b/a

Product of zeroes = c/a

Also,

x² + (b/a)x + c/a = x² - (A + B)x + AB

Hence proved

Hope you understood it........All the best